Method and unit for computing charging efficiency and charged electrical quantity of battery

ABSTRACT

A charging efficiency, which is a ratio of an electrical quantity charged in a battery as an electromotive force to a total electrical quantity supplied to the battery, is computed at a plurality of measuring points between a start and an end of charging of the battery. A resistance difference of the battery between a resistance at the charge start point and a resistance at one of the measuring points is obtained, and a full charged state resistance is obtained at a full charged state of the battery. By using a ratio of the resistance difference to the full charged state resistance, a charging efficiency of the battery is computed at the one of the measuring points. The battery is in an active state where no passivating film is formed on poles of the battery. A charged electrical quantity of the battery is obtained based on the charging efficiencies sequentially obtained during the charging of the battery when the battery is in the active state. In the mean time, a charged electrical quantity of the battery is obtained based on an integration of a charging current multiplied by a corresponding charging time during a transition period in which a passivating film remains on the poles of the battery before the charging current sufficiently breaks the passivating film.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to a method and a unit for computing acharging efficiency of a battery used for supplying an electrical powerto a load at any point between a start and an end of charging of thebattery. The charging efficiency is defined as a ratio of an electricalquantity charged in the battery to a total electrical quantity suppliedto the battery. The invention also relates to a method and a unit forknowing an electrical quantity charged in the battery based on aplurality of the obtained charging efficiencies.

2. Related Art

For example, in a battery mounted on a motor car, particularly in anelectric car having an electric motor as a primary driving unit, it isgreatly important to monitor a state of charge (SOC) of the battery toensure a normal operation condition of the car.

Recently, in a general car having an engine as a driving unit or in ahybrid car having an electric motor for providing an additional drivingforce to an engine, it has been developed to have an idling functionduring an engine stop condition, e.g. when the car must temporally stopat an intersection of roads according to a stop signal.

A car having such an idling function requires a battery which can have adischarging capacity enough for restating its engine after the batteryhas discharged a considerable amount of electrical power for driving apower assisting motor (cell motor) during an idling operation of thecar.

Therefore, it is greatly important to correctly know a state and aremaining discharging capacity of a battery concerning a general car anda hybrid car as well as the electric motor car described above.

In a typical electric car, a battery is charged during a non-usage stateof the car, e.g. in a garage. In the meantime, a hybrid car has a motorgenerator which functions a generator to charge a battery when the caris running by a primary engine. The motor generator can also charge thebattery at a deceleration period of the car even when the car is runningby the driving force of the motor generator. A general car having only aprimary engine charges its battery by an alternator driven by theengine.

Accordingly, regardless of the car type such as an electric car, ageneral car, or a hybrid car, it is important to correctly know acharged state of its battery, because the charged state varies with acharging operation as well as an electrical power supply to a load.

However, a chemical reaction during charging of a battery generates anoxygen gas and a hydrogen gas which are reduced into H₂O, so that anelectrical quantity supplied into the battery is not partially used forcharging the battery. Furthermore, this tendency is more apparent whenthe battery gets nearer to its full charged state. Thus, a mereintegration of charging currents with corresponding times can not obtaina correct charged state of the battery at a point during the charging ofthe battery.

The above-mentioned problem is not limited in an on-vehicle battery butalso appears in a general battery supplying an electrical power to aload.

SUMMARY OF THE INVENTION

In view of the above-mentioned situation, an object of the invention isto provide a method and a unit for obtaining a charging efficiency of abattery used for supplying an electrical power to a load at any pointbetween a start and an end of charging of the battery. The chargingefficiency is defined as a ratio of an electrical quantity charged inthe battery to a total electrical quantity supplied to the battery. Theinvention also provides a method and a unit for correctly computing anelectrical quantity charged in the battery. This can correctly know acharged state of the battery at any point of charging of the battery.

For achieving the object, a first aspect of the invention is a methodfor computing a charging efficiency, which is a ratio of an electricalquantity charged in a battery as an electromotive force to a totalelectrical quantity supplied to the battery, at any one point in timebetween a start and an end of charging of the battery, the methodcomprising:

measuring an initial resistance of the battery at the start of thecharging,

measuring a voltage and a current between a pair of terminals of thebattery at the one point to obtain an inner resistance of the battery atthe one point,

obtaining a resistance difference which is a difference of the innerresistance at the one point and the initial resistance, and

obtaining a ratio of the resistance difference to a full charged stateresistance that is a resistance of the battery at a full charged stateof the battery,

whereby, a charging efficiency of the battery at the one point iscomputed based on the ratio.

Thus, a voltage and a current are measured between the pair of terminalsof the battery at a plurality of measuring points between a start and anend of charging of the battery, to obtain an resistance of the batteryat each of the measuring points. Then, a resistance difference, which isa difference of a resistance at the charge start point and a resistanceat one of the measuring points, is obtained. Furthermore, a full chargedstate resistance at a full charged state of the battery is obtained, anda ratio of the resistance difference to the full charged stateresistance is obtained to know a charging efficiency of the battery ateach of the measuring points during charging of the battery. This cancorrectly know a charged state of the battery, which would be variedwith a gas generated in the battery. That is, the charging efficiencyincludes a charging loss due to the gas generation varying with acharging stage.

In a second aspect of the invention according to the first aspect, theratio of the resistance difference to the full charged state resistanceis deducted from 1 (one) to provide a charging efficiency at the onepoint.

Thus, a drop of the charging efficiency from an ideal value can becomputed at any point during the charging by using the terminal voltageand the discharging current which are measured during the charging.

A third aspect of the invention is a method for computing a chargedelectrical quantity of the battery according to the first aspect of theinvention, wherein a charged electrical quantity stored in the batteryat the charging end of the battery is obtained by using a plurality ofthe charging efficiencies each obtained at each of a plurality of themeasuring points in time between the start and the end of charging ofthe battery.

In the third aspect of the invention, a charged electrical quantity atany point during charge of the battery is obtained based on the chargingefficiencies sequentially obtained over the start and the end ofcharging of the battery according to the first aspect of the invention.

Thus, an electrical quantity actually charged in the battery as comparedwith an electrical quantity supplied to the battery is correctlycomputed at each selected point during a time interval. An integrationof the charged electrical quantities from the start to the end of thecharging correctly provides a final electrical quantity charged in thebattery.

A fourth aspect of the invention is a method for computing a chargedelectrical quantity according to the first aspect of the invention,wherein the battery has poles that are in an active state where nopassivating film is formed on the poles, and whether the poles are inthe active state is determined based on a pattern of the chargingcurrent varying with time during the charging,

the charged electrical quantity charged in the battery being obtained byusing a plurality of the charging efficiencies each obtained at each ofa plurality of the measuring points in time between the start and theend of charging of the battery when the poles are in the active state,

the charged electrical quantity of the battery being obtained based onan integration of a charging current multiplied by a correspondingcharging time during a transition period in which a passivating filmremains on the poles of the battery before the charging currentsufficiently breaks the passivating film.

The battery is not in an active state when a passivating film is formedon poles of the battery at the start of charging of the battery. In theinactive state, a charging current becomes smaller so that no gas isgenerated in the battery. With the charging operation, the passivatingfilm breaks so that the charging current increases.

Thus, the charged electrical quantity of the battery is obtained basedon an integration of the charging current multiplied by a correspondingcharging time during a transition period in which the battery is in aninactive state. In the meantime, the charged electrical quantity of thebattery is obtained based on the charging efficiencies sequentiallyobtained over the start and the end of charging of the battery when thebattery is in the active state where no passivating film remains on thepoles of the battery.

Referring to FIG. 1, a fifth aspect of the invention will be discussed.The invention is a unit for computing a charging efficiency, which is aratio of an electrical quantity charged in a battery 13 as anelectromotive force to a total electrical quantity supplied to thebattery, at any one point in time between a start and an end of chargingof the battery, the unit comprising:

a measuring device A for measuring a voltage and a current between apair of terminals of the battery at the one point to obtain an innerresistance of the battery at the one point,

an initial resistance computing device 23A for obtaining an innerresistance of the battery at the charging start based on a terminalvoltage and the corresponding current which are measured by themeasuring device,

an on-charging resistance computing device 23B for obtaining an innerresistance of the battery at the one point based on a terminal voltageand a corresponding current which are measured by the measuring device,

a resistance difference computing device 23 c for obtaining a differencebetween of the inner resistance at the one point and the initialresistance,

a storage device 23 cA for storing an inner resistance at a full chargedstate of the battery, and

a resistance ratio computing device 23D for obtaining a ratio of theresistance difference to the full charged state resistance,

whereby, a charging efficiency of the battery at the one point iscomputed based on the ratio.

In the fifth aspect of the invention, the measuring device A measures avoltage and a corresponding current between a pair of terminals of abattery 13 at a plurality of measuring points between a start and an endof charging of the battery. The resistance computing device 23A or 23Bobtains a resistance of the battery at each of the measuring pointsbased on the voltages and the corresponding currents between the pair ofterminals of the battery. The resistance difference computing device 23Cobtains a resistance difference which is a difference of a resistance atthe charge start point and a resistance at one of the measuring points.The storing device 23 cA stores a reference full charged stateresistance at a full charged state of the battery, and the resistanceratio computing device 23D obtains a ratio of the resistance differenceto the reference full charged state resistance. This can correctly knowa charged state of the battery 13, which would be varied with a gasgenerated in the battery.

Thus, a battery charging efficiency at any point during the charging iscorrectly computed by using the terminal voltage and the dischargingcurrent which are measured during the charging. The charging efficiencyincludes a charging loss due to the gas generation varying with acharging stage.

A sixth aspect of the invention is a unit for computing a chargingefficiency according to the fifth aspect of the invention wherein theresistance ratio computing device deducts the ratio of the resistancedifference to the full charged state resistance from 1 (one) to providea charging efficiency of the battery at the one point.

Thus, a drop of the charging efficiency from an ideal value can becomputed at any point during the charging by using of the terminalvoltage and the discharging current which are measured during thecharging.

A seventh aspect of the invention is a unit for computing a chargedelectrical quantity according to the fifth aspect of the invention,wherein a charged electrical quantity stored in the battery at thecharging end of the battery is obtained by using a plurality of chargingefficiencies each obtained at each of a plurality of sequential pointsin time between the start and the end of charging of the battery bymeans of the charging efficiency computing unit.

In the seventh aspect of the invention, a charged electrical quantity atany point during charge of the battery 13 is obtained based on thecharging efficiencies sequentially obtained over the start and the endof charging of the battery 13. Thus, an integration of a chargedelectrical quantity from the start to any point of the charging providesa charged electrical quantity at the charging point, obtaining a correctelectrical quantity actually charged in the battery by an electricalpower supplied into the battery 13.

Thus, an integration of the charged electrical quantity from the startto the end of the charging provides a final electrical quantity chargedin the battery.

An eighth aspect of the invention is a unit for computing a chargedelectrical quantity according to the fifth aspect of the invention,wherein the battery has poles that are in an active state where nopassivating film is formed on the poles, and the charged electricalquantity computing unit further comprises:

an active state determining device 23E for determining whether the polesare in the active state based on a pattern of the charging currentvarying with time during the charging, the charging current obtained bythe measuring device, the charged electrical quantity charged in thebattery being obtained by using a plurality of charging efficiencieseach obtained at each of a plurality of sequential points in timebetween the start and the end of charging of the battery when the polesare in the active state, and

a charged electrical quantity computing device 23F for obtaining acharged electrical quantity during a transition period in which apassivating film remains on the poles of the battery so that the polesare not in the active state before the charging current sufficientlybreaks the passivating film, the charged electrical quantity of thebattery being obtained based on an integration of a charging currentmultiplied by a corresponding charging time during the transitionperiod.

The battery 13 is not in an active state when a passivating film isformed on poles of the battery at the start of charging of the battery.In the inactive state, a charging current becomes smaller so that nodecrease of the charging efficiency of the battery due to a gasgenerated in the battery occurs. With the charging operation, thepassivating film breaks so that the charging current increases. Theactive state determining device 23E determines whether the battery is inthe active state based on a pattern of the charging current varying withtime.

Thus, the charged electrical quantity of the battery 13 is obtainedbased on an integration of the charging current with a correspondingcharging time during a transition period in which the battery 13 is inan inactive state. Therefore, an electrical quantity charged in thebattery is correctly computed during a transition period until thepassivating film is completely broken by the supplied current. In themeantime, the charged electrical quantity of the battery 13 is obtainedbased on the charging efficiencies sequentially obtained over the startand the end of charging of the battery 13 when the battery 13 is in theactive state where no passivating film remains on the poles of thebattery 13.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a block diagram showing a unit for computing a chargingefficiency and a charged electrical quantity of an on-vehicle batteryaccording to the present invention;

FIG. 2 is a schematic block diagram of a unit for obtaining a chargedelectrical quantity of an on-vehicle battery to which a method formeasuring a charging efficiency according to a first embodiment of thisinvention is applied;

FIG. 3 is a graph showing a relationship between a charging current anda corresponding time;

FIG. 4 is a schematic diagram showing an equivalent circuit of thebattery at a charging start point;

FIG. 5 is a schematic diagram showing an equivalent circuit of thebattery at a point after the charging start;

FIG. 6 is a graph showing a discharging current varying with time inrespect of the battery of which a charged electrical quantity iscomputed by a charged electrical quantity computing unit of FIG. 2;

FIG. 7 is a graph showing an example of a voltage-currentcharacteristic, which is expressed by an approximate linear equation;

FIG. 8 is a graph showing an example of a voltage-currentcharacteristic, which is expressed by an approximate quadratic equation;

FIG. 9 is a graph showing an example of polarization (voltage) varyingwith current of a battery;

FIG. 10 is a graph showing examples of the approximate characteristiccurves represented by two quadratic approximate equations, which areobtained during a discharging pattern of the battery;

FIG. 11 is a graph for explaining the method for defining two optionalpoints on the two approximate characteristic curves;

FIG. 12 is a graph for explaining the manner for defining an assumedpoint on one of the approximate characteristic curve and the manner forcorrecting the gradient between two points;

FIG. 13 is a graph for explaining the manner for defining an assumedpoint for the other approximate characteristic curve and the manner forcorrecting the gradient between two points;

FIGS. 14 and 15 illustrate a flowchart showing the processing executedby a microcomputer of FIG. 2 in accordance with a predetermined programstored in a ROM of the microcomputer;

FIG. 16 is a graph for explaining the manner of defining two points ontwo approximate characteristic curves in a second process;

FIG. 17 is a graph for explaining the manner for defining an assumedpoint for the one approximate characteristic curve and the manner forcorrecting the gradient between two points in the second process; and

FIG. 18 is a graph-for explaining the manner for defining an assumedpoint for the other approximate characteristic curve and the manner forcorrecting the gradient between two points in the second process.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

Referring to the accompanied drawings, a method and a unit for computinga charging efficiency of a battery according to the invention and forknowing an electrical quantity charged in the battery will be discussed.

FIG. 2 is an explanatory view, which is partially a block diagram, toshow generally an embodiment of a method and a unit for obtaining acharging efficiency of an on-vehicle battery according to the inventionand for knowing an electrical quantity charged in the battery. Referencenumeral 1 designates the unit which is mounted on a hybrid car having amotor generator 5 in addition to an engine 3.

In a normal operation of the hybrid car, an output of the engine 3 istransmitted to wheels 11 via a drive shaft 7 and a differential gear box9 for moving the car. In a high load condition of the car, the motorgenerator 5 is moved as a motor by an electrical power supplied from thebattery 13, and a driving force of the motor generator 5 is delivered tothe wheels 11 via the drive shaft 7 in addition to the output of theengine 3.

The motor generator 5 of the hybrid car functions as a generator at adeceleration or braking state of the car for converting a kinetic energyto an electrical power for charging the battery 13 mounted on the carfor operating various types of loads.

The motor generator 5 also functions as a cell motor that forcedlyrotates a flywheel of the engine 3 at the start of the engine 3 when astarter switch (not shown) is turned on.

In the hybrid car, a first turning step of a key (not shown) received ina cylinder (not shown) turns on accessory switches (not shown), and asecond turning step of the key turns on an ignition switch (not shown)while the accessory switches keep their on-states.

Furthermore, a third turning step of the key turns on the starter switchwhile the accessory switches and the ignition switch keep theiron-states.

The releasing of the key which has been in the third step returns thekey to the second turning step, which turns off the starter switch. Atthis stage, the key keeps its position where the accessory switches andthe ignition switch keep their on-states unless the key is turnedoppositely. At the first stage, the key also keeps its position wherethe accessory switches keep their on-states unless the key is turnedoppositely.

When the motor generator 5 functions as the cell motor, a dischargecurrent of about 250 A (ampere) flows instantaneously from the battery13 for starting the engine 3 with no other electrical units beingworking.

The battery charged electrical quantity computing unit 1 of theembodiment has a current sensor 15 and a voltage sensor 17. The currentsensor 15 senses, for example, a discharging current I flowing out fromthe battery 13 to the motor generator 5 when the motor generator 5functions as the cell motor and a charging current flowing from themotor generator 5 to the battery 13 when the motor generator 5 functionsas the generator. The voltage sensor 17 senses a voltage between a pairof terminals of the battery 13. The voltage sensor 17 having anextremely large resistance is connected to the battery 13 in parallel.

The current sensor 15 and the voltage sensor 17 are positioned in acircuit closed when the ignition switch is on.

The battery charged electrical quantity computing unit 1 of theembodiment also has a microcomputer 23 and a nonvolatile memory (NVM)25. The microcomputer 23 receives outputs from the current sensor 15 andthe voltage sensor 17 via an interface circuit 21 (called as I/F) havingan A/D converter function.

The microcomputer 23 includes CPU 23 a, RAM 23 b, and ROM 23 c. CPU 23 ais connected to RAM 23 b, ROM 23 c, and I/F 21. CPU 23 a receives asignal indicating an on or off state of the ignition switch (not shown)

RAM 23 b has a data area for storing various kinds of data and a workingarea for executing various kinds of processes. ROM 23 c stores a controlprogram for making CPU 23 a execute the processes. In ROM 23 c, a fullcharged state resistance of the battery 13 has been preliminarilystored. The full charged state resistance is the sum of a pureresistance Rf and a polarization (activation and concentration)resistance Rpolf when the battery 13 is in an initial full chargedstate.

The ROM 23 c of the battery charged electrical quantity computing unit 1corresponds to the full charged state resistance storing device 23 cAdescribed in FIG. 1.

The microcomputer 23 becomes in a sleeping mode in which a minimumnumber of processes are carried out by a dark current supplied from thebattery 13 when the ignition switch is in an off state. Themicrocomputer 23 wakes up to become in a normal active mode when theignition switch is turned on.

Next, some general discussions will be made about a charging efficiencyof the battery 13 and a charging efficiency computing method duringcharging of the battery 13.

When the battery 13 is charged under a predetermined charging voltageV_(T), the application of the predetermined charging voltage V_(T)breaks an insulative passivating film which has been formed on poles ofthe battery 13 during a non-working period of the battery 13. Thepassivating film gradually decreases and diminishes under thepredetermined charging voltage V_(T).

As illustrated in FIG. 3, a charging current I_(CHG) corresponding tothe predetermined charging voltage V_(T) does not flow simultaneouslywith the charging start of the battery 13. The charging current I_(CHG)increases toward the value corresponding to the predetermined chargingvoltage V_(T) with the passivating film being broken so that the polesof the battery becomes better in conductivity.

While the charging current I_(CHG) of the battery 13 is increasingtoward the value corresponding to the predetermined charging voltageV_(T), the charging current I_(CHG) is at a lower level so that nodecrease of the charging efficiency due to a gas generated in thebattery 13 occurs. Thus, the battery 13 is charged effectively incharging current until the charging current I_(CHG) reaches the valuecorresponding to the predetermined charging voltage V_(T).

In the meantime, after the charging current I_(CHG) has reached thevalue corresponding to the predetermined charging voltage V_(T), thepassivating film has been completely broken so that there is no effectof the passivating film. Under the application of the predeterminedcharging voltage V_(T), the charging current I_(CHG) of the battery 13is effected by an impedance increase related to a voltage increase ΔE₀of an inner electromotive voltage E₀ of the battery 13 and an innerresistance R+Rpol of the battery 13.

Until the charging current I_(CHG) of the battery 13 reaches the maximumvalue corresponding to the predetermined charging voltage V_(T) with theprogress of breaking of the passivating film, the inner electromotivevoltage E₀ increases by ΔE₀ that is very small. Thus, the resistance ofthe battery 13 is substantially equal to the inner resistance R+Rpol ofthe battery 13.

In the meantime, when no passivating film is formed on the poles of thebattery 13, the charging current I_(CHG) corresponding to thepredetermined charging voltage V_(T) flows just after the chargingstart. Thus, the resistance of the battery 13 becomes substantiallyequal to the inner resistance R+Rpol of the battery 13 just after thecharging start.

Thus, when no passivating film is formed on the poles of the battery 13,the charge of the battery 13 begins just after the application of thepredetermined charging voltage V_(T). When a passivating film is formedon the poles of the battery 13, the charge of the battery 13 beginsafter the passivating film has been completely broken by the applicationof the predetermined charging voltage V_(T) so that the charging currentI_(CHG) of the battery 13 has reached the maximum value corresponding tothe predetermined charging voltage V_(T). Accordingly, as illustrated inFIG. 4, the battery 13 is replaced by a circuit having a pure resistanceR_(O), a polarization resistance R_(pol0), and an electromotive voltageE₀ which are connected in series.

During the charge of the battery 13 under the application of thepredetermined charging voltage V_(T), the inner electromotive voltage E₀increases by an increase ΔE₀ so that R_(O)+R_(pol0) decreases intoR′+R_(pol′) (R′<R_(O), R_(pol′)<R_(pol0)).

It may be assumed that the increase ΔE₀ is due to an impedance increaseR_(E0) in the battery. Thus, as illustrated in FIG. 5, the circuit equalto the battery 13 is changed to a circuit having an inner electromotivevoltage E₀, an impedance increase R_(E0), a pure resistance R′, and apolarization resistance R_(pol′) which are connected in series.

If the charging efficiency is an ideal value of 100%, a total electricalquantity supplied into the battery 13 is completely used for chargingthe battery 13. In the equivalent circuit shown in FIG. 5, ΔE₀ decreasesa voltage drop due to the pure resistance and the polarizationresistance.

Thus, the following equation is obtained concerning the battery innerresistance of the battery 13.

R _(E0) +R′+R _(pol′) =R _(O) +R _(pol0)

(R _(E0) +R′+R _(pol′))×I _(CHG)=(R _(O) +R _(pol0))×I _(CHG0)

At the start point of the charging of the battery 13, the battery innerresistance (R_(O)+R_(pol0)) is constant. Therefore, during the chargingof the battery 13, the battery inner resistance (R_(E0)+R′+R_(pol′)) isalso constant.

However, the charging efficiency of the battery 13 is not 100% actually.Because, the charging of the battery 13 generates oxygen and hydrogengases which are changed into H₂O, so that an electrical quantitysupplied to the battery 13 is not partially stored in the battery 13.

Due to the gas generation, the battery inner resistance of the battery13 is increased by R_(GAS) corresponding to the gas generation. That is,the battery inner resistance becomes R_(E0)+R′+R_(pol′)+R_(GAS).

Furthermore, the gas generation increases while the charging of thebattery 13 advances toward its full charged state, so that the gasresistance R_(GAS) varies with the charged state of the battery 13. FIG.6 shows the inner resistance of the battery 13 which varies with acharging time during a constant voltage charging of the battery 13. Thebattery inner resistance of the battery 13 increases by R_(GAS) fromR_(O)+R_(pol0) that is a resistance value at the charging start untilthe battery 13 reaches its full charged state.

Thus, in the constant voltage charging of the battery 13 under thepredetermined charging voltage V_(T), the battery inner resistance(R″+Rpol″) increases from R_(O)+R_(pol0) which is a resistance value atthe charging start until the battery 13.

Therefore, the current I_(CHG) flown into the battery 13 (called asI_(CHG(measured)) herein) is larger than the I_(CHG) used for chargingthe battery 13 (called as I_(CHG(effective)) herein). The differencebetween I_(CHG(measured)) and I_(CHG(effective)) is indicated by I_(GAS)corresponding to the aforementioned gas generation of the battery 13 asshown by the following equation.

I _(CHG(measured)) =I _(CHG(effective)) +I _(GAS)

The charging efficiency of the battery 13 is obtained by the followingequation.

Charging Efficiency=(I _(CHG(effective)) /I _(CHG(measured))×)100%

The I_(CHG(measured)) can be obtained from an output of the currentsensor 15. However, I_(CHG(effective)) can not be measured actually, sothat I_(GAS) can not be obtained also. Therefore, another factor whichcan be measured is required for obtaining I_(GAS).

The larger the R_(GAS) becomes the smaller the I_(CHG(effective))becomes. When the battery 13 reaches its full charged state where theR_(GAS) becomes the maximum, almost all of the I_(CHG) is used for thegas generation, so that the battery 13 is no longer charged.

That is, in the full charged state, an electrical power supplied to thebattery 13 is used for the gas generation, so that the chargingefficiency is zero.

At any point during the charging of the battery 13, R_(GAS) represents avalue which is not charged in the battery 13. Thus, the ratio of R_(GAS)to R_(GAS)f that is R_(GAS) at the full charged point relates a drop ofthe charging efficiency of the battery 13.

When the charging efficiency is 100%, the battery inner resistance(R_(E0)+R′+R_(pol′)) is equal to the value (R_(O)+R_(pol0)) at thecharging start.

The battery inner resistance of the battery 13 at any point during thecharging of the battery 13 is indicated by R″+R_(pol)″. Thus, thefollowing equation is obtained.

R _(GAS″)=(R″+R _(pol″))−(R _(O) +R _(pol0))

At the full charged point of the battery 13, the battery innerresistance (R_(E0)+R′+R_(pol′)) is negligibly smaller than R_(GAS). Thatis:

R _(GAS) >>R _(E0) +R′+R _(pol′)

In the meantime, at the full charged state of the battery 13, thebattery inner resistance (Rf+Rpolf) is equal to the aforementionedformula (R_(E0)+R′+R_(pol′+R) _(GAS)).

Rf+Rpolf=R _(E0) +R′+R _(pol′) +R _(GAS)

Thus, at the full charged state of the battery 13:

R _(GAS) >>R _(E0) +R′+R _(pol′), and

Rf+R _(pol) f=R _(E0) +R′+R _(pol′) +R _(GAS)

Thus, the following formula is obtained.

Rf+R _(pol) f≈R _(GAS)

This shows that the full charged state resistance (Rf+R_(pol)f) isreplaced by R_(GAS)f.

Therefore, R_(GAS)″/R_(GAS)f is obtained as follows:

[(R″+Rpol″)−(R_(O)+R_(pol0))]/(Rf+Rpolf)

Therefore, a charging drop ratio is obtained by the following formula.

[(R″+R_(pol)l″)−(R_(O)+R_(pol0))]/(Rf+R_(pol)f)

The charging drop ratio is deducted from 1 (one) to obtain the chargingefficiency of the battery 13. That is, the charging efficiency (%) ofthe battery 13 at any point during the charging is obtained by:

{1−[[(R″+R_(pol)″)−(R_(O)+R_(pol0))]/(Rf+R_(pol)f)]}×100%

The charging efficiency and the charging efficiency computing method ofthe battery 13 have been discussed as mentioned above.

Next, a method for obtaining the battery inner resistance (R+R_(pol)) ofthe battery 13 will be discussed. The battery inner resistance isnecessary for obtaining the charging efficiency of the battery 13. Rdesignates a pure resistance and R_(pol) designates a polarizationresistance of the battery 13.

When no passivating film is formed on poles of the battery 13, thefollowing equation is provided concerning the predetermined chargingvoltage V_(T), an inner electromotive force E, an inner resistance(R+R_(pol)), and a charged electrical quantity.

V _(T) −E=(R+R _(pol))×I _(CHG)

Thus, the inner resistance (R+R_(pol)) of the battery 13 is obtained asfollows:

(R+R _(pol))=(V _(T) −E)/I _(CHG)

Next, how to obtain a battery electromotive force E of the battery 13before the charging start will be discussed. The E is necessary forobtaining a battery inner resistance (R+R_(pol)).

The battery electromotive force E of the battery 13 before the chargingstart is equal to an open circuit voltage OCV at this stage.

Therefore, a process for obtaining the battery electromotive force E ofthe battery 13 before the charging start will be discussed hereinafter.

First, during the discharging of the battery 13, a discharging current Iand a terminal voltage V of the battery 13 are periodically measured bythe current sensor 15 and the voltage sensor 17. Outputs from thecurrent sensor 15 and the voltage sensor 17 are stored after an A/Dconversion process through the I/F 21. The measured data is used forcalculating a pure resistance R and a voltage-current characteristicrelated to the pure resistance R of the battery 13 with no effect ofpolarization of the battery 13.

Furthermore, a voltage-current characteristic including an effect ofpolarization of the battery 13 is calculated from data of a terminalvoltage V and a discharging current I which are measured during thedischarging, particularly during a current decreasing period of thedischarging of the battery 13.

Then, an estimated voltage Vn that is an open circuit voltage of thebattery 13 is calculated from the V-I characteristic not including apolarization effect and the V-I characteristic including a polarizationeffect of the battery 13.

First, a general characteristic of the battery will be discussedhereinafter.

A 12 V car, a 42 V car, an electric car, or a hybrid car incorporates aload which requires a large current, such as a starter motor, a motorgenerator, a running motor, etc., and examples of the voltage-current(V-I) characteristic of a battery for supplying the electric power tothese loads are shown in FIGS. 7 and 8.

The V-I characteristic of the battery can be approximated by a linearequation: V=aI+b. However, in this embodiment, considering the influenceof the characteristic of non-linearity of the polarization component asshown in FIG. 8, a quadratic approximate equation with high correlation:V=aI2+bI+c is used. This equation can be obtained by a least-squaresmethod.

While the load which requires a large current is driven, a dischargingcurrent flowing when the battery is discharged once increasesmonotonously to exceed a prescribed value and decreases monotonouslyfrom the maximum value to the prescribed value or lower. The dischargingcurrent and the terminal voltage of the battery at this time aremeasured periodically to acquire the real data indicative of thecorrelation between the terminal voltage and discharging current. On thebasis of the data, as shown from the graph of FIG. 10, characteristiccurves (hereinafter also referred to as approximate curves) arerepresented by two approximate equations M1 and M2. The firstapproximate equation M1 represents the V-I characteristic for anincreasing discharging current which increases, after the discharginghas been started, to reach a maximum value and the V-I characteristicfor a decreasing current which decreases from the maximum value. Theequation described in FIG. 10 is an example of a concrete approximateequation obtained by the real data. The difference between these twoapproximate equations M1 and M2 will be analyzed.

In the case of the first approximate equation M1, using, as a standard,the polarization resistance component at the start of discharging, whenthe current increases after the discharging has been started, thepolarization resistance component increases gradually. When the currentreaches the maximum value, the polarization resistance component reachesthe peak. Thereafter, the polarization is gradually dissolved with adecrease in the current. However, actually, the polarization resistancecomponent is not dissolved in proportion to a decrease in the current,but the reaction is delayed. Therefore, in the approximate equation M2,the same V-I characteristic as when the current increases is notexhibited, but a larger voltage drop is generated. Thus, two approximateequations M1 and M2 corresponding to when the voltage increases and whenit decreases are acquired.

Now referring to FIGS. 11 to 13, an explanation will be given of themethod of measuring the pure resistance of a battery using twoapproximate curve equations M1 and M2 of the above V-I characteristic.

First, a point A is set within a range of the real data on theapproximate curve represented by M1. A voltage drop ΔV1 from interceptC1 of the approximate curve M1 for the ordinate of the graph of FIG. 11to point A is acquired. The value when the ΔV1 is divided by the currentI1 at point A is a combined resistance that is a sum of the pureresistance R and the polarization resistance component R_(pol) 1.Namely,

R+R _(pol) 1=ΔV 1/I 1

Likewise, as seen from the graph of FIG. 11, point B is set within arange of the real data on the approximate curve represented by M2. Avoltage drop ΔV1 from intercept C2 of the approximate curve M2 for theordinate of the graph of FIG. 11 is acquired. The value when the ΔV2 isdivided by the current I2 at point B is a combined resistance that is asum of the pure resistance R and the polarization resistance componentR_(pol) 2. Namely,

R+R _(pol) 2=ΔV 2/I 2

The difference ΔR between the combined resistances at points A and B isrepresented by

ΔR=R+R _(pol) 1−(R+R _(pol) 2)=R _(pol) 1−R _(pol) 2

This value represents a difference in the polarization resistance atpoints A and B. Therefore, it is apparent that the pure resistance Rduring the discharging does not vary.

Incidentally, as shown in FIG. 12, point A′ with a value (R+R_(pol) 1′)equal to the combined resistance (R+R_(pol) 2) at point B selected onthe approximate curve M2 is located on the approximate curve M1.Further, as shown in FIG. 13, point B′ with a value (R+R_(pol) 2′) equalto the combined resistance at point A selected on the approximate curveM1 is located on the approximate curve M2. Namely, point A′ whereR+R_(pol) 1′=R+R_(pol) 2 is located on the approximate curve M1, whereaspoint B′ where R+R_(pol) 1=R+R_(pol) 2′ is located on the approximatecurve M2.

In short, assuming that the current and voltage at point A′ are I1′ andV1′, and that the current and voltage at point B′ are I2′ and V2′, thepolarization resistances at point A′ of the coordinates (I′, V1′) and atpoint B of the coordinates (I2, V2) are equal to each other, and thepolarization resistances at point A of the coordinates (I1, V1) and atpoint B′ of the coordinates (I2′, V2′) are equal to each other.

An explanation will be given of the manner of computing the current I1′and voltage V1′ at point A′ with the resistance equal to the combinedresistance (R+R_(pol) 2) at point B which is used as a standard.

The voltage drop ΔV1′ from intercept C1 of the approximate curve M1 forthe ordinate to point A′ can be expressed by

ΔV 1′=C 1−(a 1 I 1′² +b 1 I 1′+C 1)=(R+R _(pol) 2)I 1′

Therefore,

−(a 1 I 1′+b 1)=R+R _(pol) 2

Thus, the current I1′ at point A′ is expressed by

I 1′=−(b 1+R+R _(pol) 2)/a 1

Since R+R _(pol) 2(=R′+R _(pol) 1′)=ΔV 2/I 2(=ΔV 1′/I 1′),

I 1′=−[b 1+(ΔV 2/I 2)]/a 1

=−[b 1+(ΔV 1′/I 1′)]/a 1

As apparent from the above equation, the voltage V1′ at point A′ isexpressed by

V 1′=a 1 I 1′² +b 1 I 1′+C 1

Thus, the coordinates (I1′+V1′) of point A′ is computed by known values.

Likewise, the current I2′ and voltage V2′ at point B′ equal to that(R+R_(pol) 1) at point A are expressed by

I 2′=−[b 2+(ΔV 2/I 2)]/a 2

=−[b 2+(ΔV 1′/I 1′)]/a 2

V 2′=a 2 I 2′² +b 2 I 2′+C 2

Thus, the coordinates (I1′, V2′) can be computed by known values.

ΔV2′ represents the voltage drop from intercept C2 of approximate curveM2 for the ordinate crosses the ordinate.

Thereafter, as seen from FIG. 12, the gradient of a line L1 connectingpoint A′ of the coordinates (I1′, V1′) of and point B of the coordinates(I2, V2) is acquired to provide the combined resistance R1. The combinedresistance R1 is acquired by dividing the voltage drop (V1′−V2) due tothe combined resistance (composed of the pure resistance and thepolarization resistance R_(pol) 2) by current difference (I1′−I2).Namely,

R 1=(V 1′−V 2)/(I 1′−I 2)

Likewise, as seen from FIG. 13, the gradient of a line L2 connectingpoint B′ of the coordinates (I2′, V2′) and point A of the coordinates(I1, V1) is acquired to provide the combined resistance R1. The combinedresistance R2 is acquired by dividing the voltage drop (V1′−V2) due tothe combined resistance (composed of the pure resistance and thepolarization resistance R_(pol) 1) by current difference (I1−I2′).Namely,

R 2=(V 1−V 2′)/(I 1−I 2′)

However, the combined resistances R1 and R2 are not coincident to pureresistances. This inconvenience can be overcome by dividing the voltagedrop exclusive of that due to the polarization resistance.

With reference to point B, assuming that the combined resistance R1 isexpressed by

R 1=R 1′+R _(pol) 2=R 1′+R _(pol) 1′,

the voltage drop produced when the current corresponding to a differencebetween the current I1′ at point A′ and the I2 at point B flows throughthe resistance R1′ should be incrementally compensated for, at thevoltage at point A′, by the voltage drop produced when a currentcorresponding to a difference between the current I1′ at point A′ andthe current I2 at point B flows through the polarization resistanceR_(pol) 1′ (or R_(pol) 2), and hence the following equation holds.

R 1′(I 1′−I 2)=[V 1′+R _(pol) 1′(I 1′−I 2)]−V 2

Hence,

R 1′(I 1′−I 2)=(V 1′−V 2)+R _(pol) 1′(I 1′−I 2)

Now, since R _(pol) 1′=ΔV 1′/I 1′−R 1′

R 1′(I 1′−I 2)=(V 1′−V 2)+(ΔV 1′/I 1′−R 1′)(I 1′−I 2)

2R 1′(I 1′−I 2)=(V 1′−V 2)+ΔV 1′/I 1′(I 1′−I 2)

As a result,

R 1′=[(V 1′−V 2)+(ΔV 1′/I 1′)(I 1′−I 2)]/2(I 1′−I 2)

Incidentally, it should be noted that (ΔV1′/I1′) can be replaced by(ΔV2/I2).

Likewise, with reference to point A, assuming that the combinedresistance R2 is expressed by

R 2=R 2′+R _(pol) 1=R 2′+R _(pol) 2′,

the voltage drop produced when the current corresponding to a differencebetween the current I1 at point A and the I2′ at point B′ flows throughthe resistance R2′ should be detrimentally compensated for, at thevoltage at point B′, by the voltage drop produced when a currentcorresponding to a difference between the current I1 at point A and thecurrent I2′ at point B′ flows through the polarization resistanceR_(pol) 2′ (or R_(pol) 1), and hence the following equation holds.

R 2′(I 1−I 2′)=V 1−[V 2′−R _(pol) 2′(I 1−I 2′)]

Hence,

R 2′(I 1−I 2′)=(V 1−V 2′)+R _(pol) 2′(I 1−I 2′)

 Now, since R _(pol) 2′=ΔV 2′/I 2′−R 2′

R 2′(I 1−I 2′)=(V 1−V 2′)+(ΔV 2′/I 2′−R 2′)(I 1′−I 2)

2R 2′(I 1−I 2′)=(V 1−V 2′)+ΔV 12/I 2′(I 1′−I 2′)

As a result,

R 2′=[(V 1−V 2′)+(ΔV 2′/I 2′)(I 1−I 2′)]/2(I 1−I 2′)

Incidentally, it should be noted that (ΔV2′/I2′) can be replaced by(ΔV1/I1).

The two resistances R1′ and R2′ have been acquired with reference to thetwo points A and B using the different polarization resistances (R_(pol)1′=R_(pol) 2) and (R_(pol) 1=R_(pol) 2′) and voltage drops ΔV1′(ΔV1) andΔV2′(ΔV2) from the different intercepts C1 and C2, and hence cannot bepure resistances. Thus, by obtaining the weighted average of bothresistances,

R=(R 1′+R 2′)/2

the real pure resistance R can be acquired.

The newer sets of the terminal voltages and the discharging currents fora prescribed time are stored for collection in a memory such as a RAMserving as a rewritable storage means. Using the sets of terminalvoltages and the discharging currents thus collected, two approximatecurves M1 and M2 which show the relationship between the terminalvoltage and the discharging current are obtained by the least squaresmethod. They are the first approximate curve M1 which shows a change ofthe voltage for an increasing discharging current, represented by aquadratic equation: V1(I)=a1I²+b1+C1 and the second approximate curve M2which shows a change of the voltage for a decreasing dischargingcurrent, represented by a quadratic equation: V2 (I)=a2I²+b2I+C2.

The first point A and the second point B are set on the firstapproximate curve M1 and the second approximate curve M2, respectively.In this case, points A and B are preferably set within a range wherereal data of the terminal voltage and the discharging current used toacquire the approximate curves reside. In this way, the correspondingpoints will not be assumed at points largely separate from the setpoints. The first point A and the second point B are preferably set onboth sides of point which provides a maximum point with maximumpolarization resistance. Thus, the assumed points are set on both sidesof the maximum point so that the accuracy of the pure resistanceacquired later can be enhanced.

The first assumed point A′ is assumed on the first approximate curve M1,and the second assumed B′ is assumed on the second approximate curve M2.As described previously, the first assumed point A′ provides the sameresistance as the second combined resistance R2 composed of the pureresistance of the battery and the second polarization resistancecomponent R_(pol) 2, which produces the second voltage drop ΔV2 when thesecond discharging current I2 corresponding to the second point B flows.The second assumed point B′ provides the same resistance as the firstcombined resistance R1 composed of the pure resistance of the batteryand the first polarization resistance component R_(pol) 1, whichproduces the first voltage drop ΔV1 when the first discharging currentI1 corresponding to the first point A flows.

When the two assumed points A′ and B′ could be assumed appropriately,the first gradient R1 of the line L1 connecting the second point B andthe first assumed point A′ is corrected by the voltage drop R_(pol) 2(I1′−I2) due to the second polarization resistance component R_(pol) 2,which are produced by the second discharging current I2 and thedischarging current I1′ at the first assumed point A′, thereby providingthe first corrected gradient R1′ exclusive of the voltage drop due tothe second polarization resistance component R_(pol) 2. Likewise, thesecond gradient R2 of the line L2 connecting the first point A and thesecond assumed point B′ is corrected by the voltage drop R_(pol) 2(I1−I2′) due to the first polarization resistance component R_(pol) 2,which are produced by the first discharging current I1 and thedischarging current I2′ at the second assumed point B′, therebyproviding the second corrected gradient R2′ exclusive of the voltagedrop due to the first polarization resistance component R_(pol) 1.

The first corrected gradient R1′ and the second corrected gradient R2are summed and the sum is averaged to provide an average gradient. Theaverage gradient thus provided is measured as a pure resistance of thebattery.

Thus obtained pure resistance R of the battery 13 is multiplied by adischarging current I which is the latest measured one to obtain aterminal voltage V due to the pure resistance. Such a voltage V isobtained for a discharging current I at each measuring point. Theplurality sets of V and I provide a linear equation V_(R)=a_(R)I+b_(R)via a least square method. The equation is only related to the pureresistance with no effect of polarization of the battery 13.

Next, within a decreasing range of the discharging current I of thebattery 13, a plurality of sets of actually measured V and I are used toobtain a linear equation V=aI+b via a least square method. The obtainedequation includes effects of polarization of the battery 13.

Then, on the line V_(R)=a_(R)I+b_(R) which includes no effects of thepolarization, a measured set of coordinates (V₁,I₁) is selected.Furthermore, the line V=aI+b which includes effects of the polarizationis shifted parallel so as to pass the point (V₁,I₁). Thereby, a shiftedline V′=aI+b′ is obtained.

From the equation V′=aI+b′, an estimated voltage Vn is obtained. Theestimated voltage Vn is added to a predetermined remaining voltage drope₀ to obtain a corrected voltage Vn′.

The corrected voltage Vn′ is equal to an open circuit voltage OCV beforethe charging of the battery 13.

An open circuit voltage OCV before the charging of the battery 13 can beobtained by another method. For example, a discharging current of thebattery 13 is periodically measured to integrate the discharging currentwith time for obtaining a charged electrical quantity in the battery 13.The charged electrical quantity is compared with a reference tablestored in ROM 23 c so that an open circuit voltage OCV can be acquired.

Next, referring to FIGS. 14 and 15, a process executed by CPU 23 aaccording to a control program stored in the ROM 23 c will be discussed.

The microcomputer 23 starts when an electrical power is supplied fromthe battery 13. As illustrated in FIG. 14, CPU 23 a determines whetherthe battery 13 is in its discharging state (step S1), for example, byconfirming that the battery 13 is connected to a discharging circuit(not shown).

When the battery 13 is not in a discharging state (N in step S1), theprocessing goes to step S5 discussed later. When the battery 13 is in adischarging state (Y in step S1), a process for calculating an opencircuit voltage OCV before the charging is carried out (step S2). Thecalculated open circuit voltage OCV of the battery 13 before charging isstored as a battery electromotive force E of the battery 13 in RAM 23 b(step S3), and step S4 determines again whether the battery 13 is in adischarging state.

When the battery 13 is in a discharging state (Y in step S4), theexecution returns to step S2. When the battery 13 is not in adischarging state (N in step S4), the execution returns to step S5.

When the battery is not in a discharging state in steps S1 and S4, theprocessing goes to steps including step S5, in which a chargingefficiency and a charged electrical quantity of the battery 13 areobtained during a charging operation.

In step S5, outputs from the current sensor 15 and the voltage sensor 17are supplied as A/D converted data through I/F 21. From digital valuesof voltages and currents, an electrical quantity charged in the battery13 from the charging start to a present point is calculated (step S6).

The electrical quantity calculated in step S7 is added to the batteryelectromotive force E stored in RAM 23 b (step S7) Outputs from thecurrent sensor 15 and the voltage sensor 17 are supplied again as A/Dconverted data through I/F 21 (step S8). Step S9 determines whether thelatest obtained current value is larger than a previous one. When thedecision is negative (N in step S9), the execution goes to step S12described later.

On the contrary, when the decision is affirmative (Y in step S9), anelectrical quantity charged in the battery 13 during a period from aprevious measuring point to a present measuring point is calculated byusing outputs from the current sensor 15 and the voltage sensor 17 (stepS10).

Then, the electrical quantity calculated in step S10 is added to thebattery electromotive force E stored in RAM 23 b (step S11) and theexecution returns to step S8.

It is noted that a charging efficiency of 100% is assumed forcalculating a charged electrical quantity in steps S6 and S10.

In step S9, when the latest output from the current sensor 15 is notlarger than a previous one, the processing goes to step S12. In stepS12, as illustrated in FIG. 15, a battery inner resistanceR_(O)+R_(pol0) of the battery 13 is obtained from a charging currentI_(CHG0), a predetermined charging voltage V_(T), and an innerelectromotive voltage E0 at the charging start as follows:

(R _(O) +R _(pol0))=(V _(T) −E ₀)/I _(CHG0)

Thus obtained battery inner resistance R_(O)+R_(pol0) is stored in RAM23 b as a battery inner resistance (step S13) before the processing goesto step S14.

In step S14, a present charging current I_(CHGA) and a presentpredetermined charging voltage V_(T) are obtained from outputs of thecurrent sensor 15 and the voltage sensor 17 after the charging start(step S14). The battery electromotive force E previously stored in RAM23 b is designated as E′. A battery inner resistance R″+R_(pol″) afterthe charging start is obtained by the following equation (step S15).

(R″+R _(pol″))=(V _(T) −E″)/I_(CHGA)

Next, step S16 obtains a charging efficiency, which is a ratio of anelectrical quantity charged in the battery 13 to a total electricalquantity flown into the battery 13, from the battery inner resistanceR″+R_(pol″) after the charging start, a full charged state resistanceRf+R_(pol)f, and the initial battery inner resistance R_(O)+R_(pol0) Thefull charged state resistance Rf+R_(pol)f has been preliminarily storedin ROM 23 c. The charging efficiency is obtained by the followingformula.

{1−[[(R″+R_(pol″))−(R_(O)+R_(pol0))]/(Rf+R_(pol)f)]}×100%

Thus obtained charging efficiency of the battery 13 is multiplied by apresent charging current I_(CHGA) obtained in step S16 and thecorresponding charging time. This provides an electrical quantitycharged in the battery 13 from the previous sampling point to thepresent sampling point, and the electrical quantity is added to thebattery electromotive force E which has been stored in RAM 23 b (stepS17). Then, step S18 determines whether the charging of the battery 13is continuing.

When the charging of the battery 13 is continuing (Y in step S18), theexecution returns to step S14 of FIG. 14. When the charging of thebattery 13 is not continuing (N in step S18) the execution returns tostep S2 of FIG. 14.

As understood from the above discussion, in the battery chargedelectrical quantity computing unit 1 of the embodiment, step S12 of theflowchart of FIG. 15 is a process corresponding to the initialresistance computing device 23A described in the summary of theinvention, and step S15 of FIG. 15 is a process corresponding to theon-charging resistance computing device 23B. Furthermore, step S16 is aprocess corresponding to the resistance difference computing device 23Cand the resistance ratio computing device 23D.

Moreover, the measuring device A described in the summary of theinvention corresponds to the current sensor 15, the voltage sensor 17,and a device for processing outputs from the current sensor 15 and thevoltage sensor 17 which includes the A/D conversion and storing of theoutputs during steps S2, S5, S8, and S14 of FIG. 14 or 15.

Furthermore, the active state computing means 23E described in thesummary of the invention corresponds to step S9 of FIG. 14, and thetransition period electrical quantity computing device 23F correspondsto step S10 of FIG. 14.

Next, operational steps of thus configured battery charged electricalquantity computing unit 1 of the embodiment will be discussed.

First, whether the battery 13 is in a charging state based on connectionstates of charging and discharging circuits with the battery 13 isdetermined. When it is determined that the battery 13 is in adischarging state, an open circuit voltage OCV corresponding to avoltage between a pair of terminals of the battery 13 which is in anequilibrium state before the start of charging is computed inconsideration of measured terminal voltages V and discharge currents Iof the battery during the discharging.

Thereafter, when the charging of the battery 13 starts after thedischarging, a charging efficiency and a charged electrical quantity ofthe battery 13 are computed.

At a stage just after the charging, when the charging current I_(CHG) isincreasing, it is supposed that an insulative passivating film formed onpoles of the battery is being gradually broken. Since the chargingcurrent is small at the stage, no gas generation occurs in the battery.Thus, an integration of the charging current I_(CHG) multiplied by acorresponding charging time provides an electrical quantity stored inthe battery 13 from the charging start, and the electrical quantity isadded to the initial electromotive force E of the battery 13.

In the meantime, when the charging current I_(CHG) is decreasing, it issupposed that there is no insulative passivating film on the poles ofthe battery 13, but there is a charging efficiency drop due to a gasgenerated in the battery. Therefore, a charging efficiency and acharging electric quantity of the battery are obtained generally afterthe charging current I_(CHG) has reached the maximum value.

A battery inner resistance of the battery 13 is obtained as an initialresistance (R_(O)+R_(pol0)) at a point where the charging currentI_(CHG) is the maximum.

After the current maximum point, a present resistance R″+R_(pol″) and aresistance difference (R″+R_(pol″))−(R_(O)+R_(pol0)) are periodicallyobtained until the charging of the battery 13 is completed.

Furthermore, a drop of the charging efficiency is obtained as a ratio ofthe resistance difference (R″+R_(pol″))−(R_(O)+R_(pol0)) to a fullcharged state resistance Rf+R_(polf). Thus, a charging efficiency at anypoint during the charging of the battery is obtained by1−[[(R″+R_(pol″))−(R_(O)+R_(pol0))]/(Rf+R_(pol)f).

After the charging completion of the battery 13, an integration of thecharging current I_(CHG), the charging efficiency, and the samplinginterval time at each measuring point is an electrical quantity storedin the battery 13 during the sampling time. An integration of theelectrical quantity from the start to the end of the battery chargingprovides a total electrical quantity charged in the battery 13.

While the breaking of a passivating film formed on the poles of thebattery is being carried out just after the charging of the battery, acharged electrical quantity charged in the battery is calculated withoutconsideration of the charging efficiency of the battery. After thebreaking completion of the passivating film, a charged electricalquantity charged in the battery is calculated with consideration of thecharging efficiency of the battery.

In the meantime, when the breaking of a passivating film formed on thepoles of the battery is not carried out, or when no passivating film hasnot been formed on the poles of the battery before the charging start,the battery is in an active state from the beginning. In the activestate, a charged electrical quantity charged in the battery iscalculated with consideration of the charging efficiency of the batteryas mentioned above.

In the battery charged electrical quantity computing unit 1 of theembodiment, an electrical quantity actually stored in the battery 13 anda charging efficiency necessary for computing a total charged electricalquantity are appropriately obtained from the terminal voltage V_(T) andthe charging current I_(CHG).

It may be practically possible that a charged electrical quantity issummed after the charging current reached the maximum, when anelectrical power supplied before the maximum point into the battery isnegligibly small.

In the embodiment, for obtaining a pure resistance R and an open circuitvoltage OCV of the battery 13, two the approximate curves M1 and M2showing V-I characteristics are applied, and points A and B each on theapproximate curve M1 or M2 are selected.

Now, referring to FIGS. 16 to 18, a second method for obtaining a pureresistance R and an open circuit voltage OCV of the battery 13 will bediscussed hereinafter. The second method uses point P in place of pointsA and B. The point P is on the approximate curve M2 as well as on theapproximate curves M1, and the discharging current is the maximum atpoint P.

As illustrated in FIG. 16, point P common to the approximate curves M1and M2 is selected. A vertical distance form intercept C1 of theapproximate curve M1 to point P is a voltage drop ΔV1. The voltage dropis caused by a pure resistance R and a polarization resistance R_(pol)1. That is:

R+R _(pol) 1=ΔV 1/Ip

Ip: a current at point P

Next, as illustrated in FIG. 16, a vertical distance form intercept C2of the M2 to point P is a voltage drop ΔV2. The voltage drop is causedby a pure resistance R and a polarization resistance R_(pol) 12. Thatis:

R+R _(pol) 2=ΔV 2/Ip

In the embodiment described above, the two optional points A and B areset within the range where there are the real data of the approximatecurves M1 and M2. However, as a modification thereof, a single point maybe set at point P corresponding to the maximum discharging current ofthe battery, which is measured to acquire the two approximate curves M1and M2. Using the common data, inclusion of an error can be suppressed.Referring to FIGS. 16 to 18, an explanation will be given of thismodification.

First, a point P corresponding to the maximum value of the dischargingcurrent of the battery is set on the two approximate curves M1 and M2. Avoltage drop ΔV1 from the intercept C1 of the ordinate in theapproximate curve M1 to point P on the approximate curves is acquired.The value obtained when the ΔV1 is divided by the current Ip at point Pis a combined resistance that is a sum of the pure resistance R and thepolarization resistance component R_(pol1). Namely,

R+R _(pol) 1=ΔV 1/Ip

Likewise, a voltage drop ΔV2 from an intercept C2 of the ordinate of theapproximate curve M2 to point P on the approximate curves is acquired.The value when the ΔV2 is divided by the current Ip at point P is acombined resistance that is a sum of the pure resistance R and thepolarization resistance component R_(pol) 2. Namely,

R+R _(pol) 2=ΔV 2/Ip

The difference ΔR between the combined resistances at point P isrepresented by

ΔR=R+R _(pol) 1−(R+R _(pol) 2)=R_(pol) 1−R_(pol) 2

This value represents a difference in the polarization resistance atpoint P of the different approximate curves. Therefore, it is apparentthat the pure resistance R when the discharging has occurred once doesnot vary.

Incidentally, as shown in FIG. 17, point P1 with a value (R+R_(pol) 1′)equal to the combined resistance (R+R_(pol) 2) at point P set on theapproximate curve M2 is located on the approximate curve M1. Further, asshown in FIG. 17, point P2 with a value (R+R_(pol) 2′) equal to thecombined resistance at point P selected on the approximate curve M1 islocated on the approximate curve M2. Namely, point P1 where R+R_(pol)1′=R+R_(pol) 2 is located on the approximate curve M1, whereas point P2where R+R_(pol) 1=R+R_(pol) 2′ is located on the approximate curve.

In short, assuming that the current and voltage at point P1 are Ip1 andVp1, and that the current and voltage at point P2 are Ip2 and Vp2, thepolarization resistances at point P1 of the coordinates (Ip1, Vp1) andpoint P of the coordinates (Ip, Vp) are equal to each other, and thepolarization resistances at point P of the coordinates (Ip, Vp) and atpoint P2 of the coordinates (Ip2, Vp2) are equal to each other.

An explanation will be given of the manner of computing the current Ip1and voltage Vp1 at point P1 with the resistance (R+R_(pol) 1′) equal tothe combined resistance (R+R_(pol) 2) at point P.

The voltage drop ΔVp1 from the intercept C1 where the approximate curveM1 crosses the ordinate to point P1 can be expressed by

ΔVp 1=C 1−(a 1 Ip 1 ² +b 1 Ip 1+C 1)=(R+R _(pol) 2)Ip 1

Therefore,

−(a 1 Ip 1+b 1)=R+R _(pol) 2

Thus, the current Ip1 at point P1 is expressed by

Ip 1=−(b 1+R+R _(pol) 2)/a 1

Since R+R _(pol) 2(=R+R _(pol) 1′)=ΔV 2/I 2(=ΔVp 1/Ip 1),

Ip 1=−[b 1+(ΔVp/Ip)]/a 1

=−[b 1+(ΔVp 1/Ip 1)]/a 1

As apparent from the above equation, the voltage Vp1 at point P1 isexpressed by

Vp 1=a 1 Ip 1 ² +b 1 Ip 1+C 1

Thus, the coordinates (Ip1, Vp1) of point P1 are computed by knownvalues.

Likewise, the current Ip2 and voltage Vp2 at point P2 with a value(R+R_(pol) 2′) equal to that (R+R_(pol) 1) at point P are expressed by

Ip 2=−[b 2+(ΔV 2/I 2)]/a 2

=−[b 2+(ΔVp 2/Ip 2)]/a 2

Vp 2=a 2 Ip 2 ² +b 2 Ip 2+C 2

Thus, the coordinates (Ip2, Vp2) can be computed by known values.

ΔVp2 represents the voltage drop from the intercept C2 where theapproximate curve M2 crosses the ordinate.

Thereafter, as seen from FIG. 17, the gradient of a line L1 connectingpoint P1 of the coordinates (Ip1, Vp1) and point P of the coordinates(Ip, Vp) is acquired to provide the combined resistance R1. The combinedresistance R1 is acquired by dividing the voltage difference (Vp1−Vp)produced by the combined resistance (composed of the pure resistance andthe polarization resistance R_(pol) 2) by current difference (Ip1−Ip).Namely,

R 1=(Vp 1−Vp)/(Ip 1−Ip)

Likewise, as seen from FIG. 18, the gradient of a line L2 connectingpoint P2 of the coordinates (Ip2, Vp2) and point P of the coordinates(Ip, Vp) is acquired to provide the combined resistance R1. The combinedresistance R2 is acquired by dividing the voltage difference (Vp−Vp2)produced by the combined resistance (composed of the pure resistance andthe polarization resistance R_(pol) 1) by current difference (Ip−Ip2)Namely,

R 2=(Vp−Vp 2)/(Ip−Ip 2)

However, the combined resistances R1 and R2 are not coincident to pureresistances. This inconvenience can be overcome by dividing the voltagedrop exclusive of that due to the polarization resistance.

With reference to point P of the approximate curve M2, assuming that thecombined resistance R1 is expressed by

R 1=R 1′+R _(pol) 2=R 1′+R _(pol) 1′,

the voltage drop produced when the current corresponding to a differencebetween the current Ip1 at point P1 and the Ip at point P flows throughthe resistance R1′ should be incrementally compensated for, at thevoltage at point P1, by the voltage drop produced when a currentcorresponding to a difference between the current Ip1 at point P1 andthe current Ip at point P2 flows through the polarization resistanceR_(pol) 1′ (or R_(pol) 2).

Hence, the following equation holds.

R 1′(I 1′−I 2)=(V 1′+R _(pol) 1′(I 1′−I 2)]−V 2

Hence,

R 1′(I 1′−I 2)=(Vp 1−Vp)+R _(pol) 1′(Ip 1−Ip)

Now, since R _(pol) 1′=ΔV 1′/Ip 1−R 1′

R 1′(Ip 1−Ip)=(Vp 1−Vp)+(ΔVp 1/Ip 1−R 1′)(Ip 1−I 2)

2R 1′(Ip 1−I 2)=(V 1′−Vp)+ΔVp 1/Ip 1(Ip 1−Ip)

As a result,

R 1′=[(Vp 1−Vp)+(ΔVp 1/Ip 1)(Ip 1−Ip)]/2(Ip 1−Ip)

Incidentally, it should be noted that (ΔVp1/Ip1) can be replaced by(ΔV2/Ip).

Likewise, with reference to point P on the approximate curve M1,assuming that the combined resistance R2 is expressed by

R 2=R 2′+R _(pol) 1=R 2′+R _(pol) 2′,

the voltage drop produced when the current corresponding to a differencebetween the current I1 at point A and the I2′ at point B′ flows throughthe resistance R2′ should be detrimentally compensated for, at thevoltage at point B′, by the voltage drop produced when a currentcorresponding to a difference between the current I1 at point A and thecurrent I2′ at point B′ flows through the polarization resistanceR_(pol) 2′ (or R_(pol) 1), and hence the following equation holds.

R 2′(Ip−Ip 2)=Vp−[Vp 2−R _(pol) 2′(Ip−Ip 2)]

Hence,

R 2′(I 1−Ip 2)=(Vp−Vp 2)+R _(pol) 2′(Ip−Ip 2)

Now, since R _(pol) 2′=ΔVp 2/Ip 2−R 2′

R 2′(Ip−Ip 2)=(Vp−Vp 2)+(ΔVp 2/Ip 2−Rp 2)(Ip−Ip 2)

2R 2′(I 1−Ip 2)=(Vp−Vp 2)+ΔVp 2/Ip 2(Ip−Ip 2)

As a result,

R 2′=[(Vp−Vp 2)+(ΔVp 2/Ip 2)(Ip−Ip 2)]/2(Ip−Ip 2)

Incidentally, it should be noted that (ΔVp/Ip) can be replaced by(ΔV1/I1).

The two resistances R1′ and R2′ have been acquired with reference to thetwo points A and B using the different polarization resistances (R_(pol)1′=R_(pol) 2) and (R_(pol) 1=R_(pol) 2′) and voltage drops ΔVp1(ΔVp) andΔVp2(ΔVp) from the different intercepts C1 and C2, and hence cannot bepure resistances. Thus, by obtaining the weighted average of bothresistances,

R=(R 1′+R 2′)/2

the real pure resistance R can be acquired.

In the method explained with reference to FIGS. 16 to 18, the singlepoint may be set at point P corresponding to the maximum dischargingcurrent of the battery, which is measured to acquire the two approximatecurves M1 and M2. Using the common data, inclusion of an error can besuppressed.

The first assumed point P1 is assumed on the first approximate curve M1,and the second assumed P2 is assumed on the second approximate curve M2.As described previously, the first assumed point P1 provides the sameresistance as the second combined resistance R2 composed of the pureresistance of the battery and the second polarization resistancecomponent R_(pol) 2, which produces the second voltage drop ΔV2 when thedischarging current Ip corresponding to point P on the secondapproximate curve M2 flows. The second assumed point P2 provides thesame resistance as the first combined resistance R1 composed of the pureresistance of the battery and the first polarization resistancecomponent R_(pol) 1, which produces the first voltage drop ΔV1 when thesecond discharging current Ip corresponding to point on the firstapproximate curve M1 flows.

When the two assumed points P1 and P2 could be assumed appropriately,the first gradient R1 of the line L1 connecting point P and the firstassumed point P1 is corrected by the voltage drop R_(pol) 2(Ip1−Ip) dueto the second polarization resistance component R_(pol) 2, which areproduced by the discharging current Ip and the discharging current Ip1at the first assumed point P1, thereby providing the first correctedgradient R1′ exclusive of the voltage drop due to the secondpolarization resistance component R_(pol) 2. Likewise, the secondgradient R2 of the line L2 connecting point P and the second assumedpoint P2 is corrected by the voltage drop R_(pol) 1(Ip−Ip2) due to thefirst polarization resistance component R_(pol) 1, which are produced bythe discharging current Ip and the discharging current Ip2 at the secondassumed point P2, thereby providing the second corrected gradient R2′exclusive of the voltage drop due to the first polarization resistancecomponent R_(pol) 1.

The first corrected gradient R1′ and the second corrected gradient R2′are summed and the sum is averaged to provide an average gradient. Theaverage gradient thus provided is measured as a pure resistance of thebattery.

This embodiment can be executed in substantially the same processing asillustrated in the flowcharts of FIGS. 14 and 15 with the firstembodiment explained with reference to FIGS. 11 to 13, except that thetwo points on the approximate curves M1 and M2 are set at the same pointcorresponding to the maximum value of the discharging current of thebattery on the two approximate curves M1 and M2.

The aforementioned embodiment uses NVM 25 as the full charged stateresistance storing device. However, such a device can be replaced byproviding an area in ROM 23 c of the microcomputer 23 for storing a fullcharged state resistance Rf+R_(pol)f.

As an embodiment of the invention, the on-vehicle battery chargedelectrical quantity computing unit 1 of the battery 13 has beendiscussed hereinabove. Of course, the present invention can be appliedto a computing unit of the battery 13 for obtaining a chargingefficiency that is a ratio of an actually charged electrical quantity toa total electrical quantity flown into the battery 13.

In the case of the on-vehicle battery charging efficiency computingunit, a battery charging efficiency (%) at each measuring point duringthe charging may be stored in a NVM. A full charged state resistanceRf+R_(polf) of the battery 13 may be also stored in the NVM.

In addition, the present invention is not limited in computing acharging efficiency and a charged electrical quantity of an on-vehiclebattery but also can be applied to a general application such as aportable telephone and a portable personal computer.

What is claimed is:
 1. A method for computing a charging efficiency,which is a ratio of an electrical quantity charged in a battery as anelectromotive force to a total electrical quantity supplied to thebattery, at any one point in time between a start and an end of chargingof the battery, the method comprising: measuring an initial resistanceof the battery at the start of the charging, measuring a voltage and acurrent between a pair of terminals of the battery at the one point toobtain an inner resistance of the battery at the one point, obtaining aresistance difference which is a difference of the inner resistance atthe one point and the initial resistance, and obtaining a ratio of theresistance difference to a full charged state resistance that is aresistance of the battery at a full charged state of the battery,whereby, a charging efficiency of the battery at the one point iscomputed based on the ratio.
 2. A method for computing a chargingefficiency according to claim 1 wherein the ratio of the resistancedifference to the full charged state resistance is deducted from 1 (one)to provide a charging efficiency at the one point.
 3. A method forcomputing a charged electrical quantity of the battery according toclaim 1, wherein a charged electrical quantity stored in the battery atthe charging end of the battery is obtained by using a plurality of thecharging efficiencies each obtained at each of a plurality of themeasuring points in time between the start and the end of charging ofthe battery.
 4. A method for computing a charged electrical quantityaccording to claim 1, wherein the battery has poles that are in anactive state where no passivating film is formed on the poles, andwhether the poles are in the active state is determined based on apattern of the charging current varying with time during the charging,the charged electrical quantity charged in the battery being obtained byusing a plurality of the charging efficiencies each obtained at each ofa plurality of the measuring points in time between the start and theend of charging of the battery when the poles are in the active state,the charged electrical quantity of the battery being obtained based onan integration of a charging current multiplied by a correspondingcharging time during a transition period in which a passivating filmremains on the poles of the battery before the charging currentsufficiently breaks the passivating film.
 5. A unit for computing acharging efficiency, which is a ratio of an electrical quantity chargedin a battery as an electromotive force to a total electrical quantitysupplied to the battery, at any one point in time between a start and anend of charging of the battery, the unit comprising: a measuring devicefor measuring a voltage and a current between a pair of terminals of thebattery at the one point to obtain an inner resistance of the battery atthe one point, an initial resistance computing device for obtaining aninner resistance of the battery at the charging start based on aterminal voltage and the corresponding current which are measured by themeasuring device, an on-charging resistance computing device forobtaining an inner resistance of the battery at the one point based on aterminal voltage and a corresponding current which are measured by themeasuring device, a resistance difference computing device for obtaininga difference between of the inner resistance at the one point and theinitial resistance, a storage device for storing an inner resistance ata full charged state of the battery, and a resistance ratio computingdevice for obtaining a ratio of the resistance difference to the fullcharged state resistance, whereby, a charging efficiency of the batteryat the one point is computed based on the ratio.
 6. A unit for computinga charging efficiency according to claim 5 wherein the resistance ratiocomputing device deducts the ratio of the resistance difference to thefull charged state resistance from 1 (one) to provide a chargingefficiency of the battery at the one point.
 7. A unit for computing acharged electrical quantity according to claim 5, wherein a chargedelectrical quantity stored in the battery at the charging end of thebattery is obtained by using a plurality of charging efficiencies eachobtained at each of a plurality of sequential points in time between thestart and the end of charging of the battery by means of the chargingefficiency computing unit.
 8. A unit for computing a charged electricalquantity according to claim 5, wherein the battery has poles that are inan active state where no passivating film is formed on the poles, andthe charged electrical quantity computing unit further comprises: anactive state determining device for determining whether the poles are inthe active state based on a pattern of the charging current varying withtime during the charging, the charging current obtained by the measuringdevice, the charged electrical quantity charged in the battery beingobtained by using a plurality of charging efficiencies each obtained ateach of a plurality of sequential points in time between the start andthe end of charging of the battery when the poles are in the activestate, and a charged electrical quantity computing device for obtaininga charged electrical quantity during a transition period in which apassivating film remains on the poles of the battery so that the polesare not in the active state before the charging current sufficientlybreaks the passivating film, the charged electrical quantity of thebattery being obtained based on an integration of a charging currentmultiplied by a corresponding charging time during the transitionperiod.